“Like any science or art, mathematics is not about how much you know about existing knowledge discovered by other mathematicians; it’s about how much you can contribute to that field. And the only way to contribute to that field is by boldly breaking existing rules that other people take for granted. As long as you don’t give up, there is hope, so you must believe in yourself. Always be ambitious, and think outside the box. That’s what made you, you; and that’s what’s going to keep you, you.”
— Ivan Zhanhu Feng
I like number theory, algebra, and geometry. I’m particularly interested in the Riemann zeta function and its related topics, which basically include the contour integration and infinite products in complex analysis, L-functions and the prime number theorem in analytic number theory, the Lichtenbaum conjectures in algebraic K-theory, and the Weil conjectures in étale cohomology.
My undergraduate thesis is on the basic properties of the Riemann zeta function as well as the origin and history of the Riemann Hypothesis, under the supervision of Dr. Yan Zhao.
My master’s thesis is on zeta functions analyzed mainly from analytic number theory and algebraic K-theory. And my thesis supervisor is Prof. Eric M. Friedlander, a world-famous K-theorist. The thesis is now available for view and download in the USC Digital Library. My thesis committee members were Prof. Eric Friedlander (Chair), Prof. Susan Montgomery, and Prof. Sheldon Kamienny.
My current temporary advisor is Prof. Kyler Siegel. In my first Ph.D. year, my MGSA mentor was Wes (Linds) Wise.
Selected papers:
A Coherent Introduction to Algebraic K-theory (11/20/2021)
Values of Zeta Functions at Integers (01/21/2022)
Zeta functions: From Prime Numbers to K-theory (04/16/2022)
Periodicity Uncovered: A Deep Dive into Bott’s Theorems in K-Theory and Fiber Bundles (5/10/2023)
More papers coming soon… 😺
Selected coursework notes:
Math 500: Ivan’s Colloquia Notes and Reports
Math 520: Ivan’s Solutions to Some Exercises from Ahlfors’s Complex Analysis
Math 532: Ivan’s Solutions to Some Exercises from Heidelberg’s A Course in Enumeration
Math 541: Ivan’s Solutions to Exercises in Heilman’s Lecture Notes
Math 595: Ivan’s Thoughts on Teaching
Math 610: Ivan’s Selected Homework Solutions
Math 641: Ivan’s Solutions to Selected Homework Problems
Graduate math courses taken at USC:
Math 500 (Graduate Colloquium) [Spring 2023];
507a, b (Theory of Probability) [Fall 2022], [Spring 2024];
510a, b (Algebra) [Fall 2020, Spring 2021];
520 (Complex Analysis) [Spring 2021];
525a, b (Real Analysis) [Fall 2020, Spring 2021];
532 (Combinatorial Analysis) [Fall 2022];
535a (Differential Geometry) [Spring 2021];
540 (Topology) [Fall 2020];
541a (Introduction to Mathematical Statistics) [Spring 2023];
555a, b (Partial Differential Equations) [Fall 2021, Spring 2022];
565a (Ordinary Differential Equations) [“Audit”, Spring 2022];
580 (Introduction to Functional Analysis) [Fall 2023];
590 (Directed Research) [Summer 2024] (In process);
594a, b, z (Master’s Thesis) [Fall 2021, Spring 2022];
595 (Practicum in Teaching the Liberal Arts: Mathematics) [Fall 2022];
605 (Topics in Probability) [Fall 2023];
610 (Topics in Algebra) [Summer 2023];
655 (Topics in Differential Equations) [Spring 2024];
641 (Topics in Topology) [Spring 2023]
More courses coming soon… 😅
Other fun work:
Proof of the Hairy Ball Theorem
An interesting extension of a basic calculus problem
Weak convergence theorems in the Theory of Probability (Zoom recordings): Part I, Part II, Notes
Exploring Leray’s Formulation of the Navier-Stokes Equations: Presentation Recording, Notes
Note: This picture was taken at Manhattan Beach, Marina del Rey in August 2022. I’ve placed it here because the view is incredibly beautiful, with a hint of mysterious and surreal atmosphere. During that trip, I was so captivated by the seaside scenery that I ended up writing two poems titled “Seashore Duet” (which can be found on the 2022 poetry page) to immortalize my memories. In August 2023, exactly one year later and just before the semester started, I revisited the same place since I was feeling nostalgic. I left another poem there, titled “Coastal Symphony” (which can be found on the 2023 poetry page).
Last update: May 29, 2024